Random Number Generation Using a Biased Source

We study random number generation using a biased source motivated by previous works on this topic, mainly, von Neumman (1951), Elias (1972), Knuth and Yao (1976) and Peres (1992). We study the problem in two cases: first, when the source distribution is unknown, and second, when the source distribution is known. In the first case, we characterize the functions that use a discrete random source of unknown distribution to simulate a target discrete random variable with a given rational distribution. We identify the functions that minimize the ratio of source inputs to target outputs. We show that these optimal functions are efficiently computable. In the second case, we prove that it is impossible to construct an optimal tree algorithm recursively, using algebraic decision procedures. Our model of computation is sufficiently general to encompass previously known algorithms for this problem.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Pae, Sung-il

Contributors dc:contributor

• Loui, Michael C.

• Engineering, Electronics and Electrical

Language dc:language

eng

Identifier

(MiAaPQ)AAI3182342

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/81665